Technical Field
The present disclosure relates to double ball-bars in measurement apparatuses and in particular to the compensation of geometric and thermal errors of double ball-bars in hexapod measurement apparatuses or machines.
Description of Related Art
A double ball-bar has precision ball and socket joints at its two ends. It is used to measure the absolute bar length or the change of bar length between the two precision balls. Its applications can be found in both machine tools and hexapod coordinate measurement machines. The displacement sensor for a double ball-bar includes linear variable differential transformer (LVDT), laser interferometer, linear magnetic encoder and linear optical encoder, and the measurement principle can be either incremental or absolute.
In the present disclosure, the distance between the centers of the two connected ball and socket joints is defined as the center distance. Like any other precision machines, the double ball-bar also has geometric and thermal errors. One example of the geometric errors is the misalignment between the sensor measuring direction and the center line connecting the two ball centers. Another geometric error is the deflection of the double ball-bar due to the gravitational force. When a double ball-bar has stiffness problem and becomes curved due to its own weight, the difference between bar length and center distance is not ignorable. For a highly accurate double ball-bar, the displacement sensor is meant to measure the center distance, not the bar length. Further, the accuracy of a double ball-bar is sensitive to ambient temperature. The measurement apparatus or machine may be used in a workshop without temperature control. A change in ambient temperature will cause the double ball-bar to expand or contract between the two ball and socket joints, which results in thermal errors in the measured center distance.
Investigations have shown that the readhead of an optical linear encoder or a magnetic linear encoder is also a heat source and may cause thermal error in the double ball-bar. Although the power of the electrical circuit in the readhead is low, the generated heat may raise the temperature of the readhead and the neighboring elements notably as their mass is small.
Because of the geometric and thermal errors, the relationship between the center distance and the measured displacement amount is non-linear and time-variant. For highly accurate applications like hexapod measurement apparatuses or machines, it is important to identify these errors and to compensate them.